1. Technical Field
The present invention relates to a simulation method and a simulation system that provide, through simulation, information on a transfer pattern of a predetermined mask pattern transferred to a wafer by optical photolithography, and to a method of modifying the mask pattern.
2. Related Art
Based on the latest progress in semiconductor device manufacturing technology, the minimum feature size of the semiconductor device has now reached 90 nm or even smaller. Such scaling has been achieved because of the progress in fine pattern formation techniques including mask process techniques, photolithography techniques and etching techniques. During the era that exposure equipments utilized an i-line (365 nm) and g-line (436 nm) and the pattern size was sufficiently larger than the light wavelength of the exposure equipments, transferring an LSI pattern on a mask as it is a plane figure of the LSI pattern to be formed on a wafer, again transferring the obtained mask pattern on the wafer by a projection optical system, and performing an etching process on the base layer could provide a pattern substantially identical to the original LSI pattern, on the wafer. The progress in scaling of the pattern, however, has made it so difficult to feasibly transfer or form the pattern in each process, that a final finishing dimension (critical dimension, hereinafter CD) can no longer reproduce the dimension (CD) of the original LSI pattern.
Especially in the lithography and etching process, which are the critical processes for attaining the highly scaled patterns, the dimensional accuracy (CD accuracy) of the pattern to be formed has come to largely fluctuate depending on the layout of other patterns disposed in the periphery of the object pattern. In order to restrain such fluctuation, an optical proximity correction (hereinafter, OPC) technique has been introduced so as to modify in advance an edge and corner portion of the mask pattern, where the fluctuation prominently takes place, so that the dimension after the process becomes the desired value.
Currently, because of the complication in the OPC technique, the LSI pattern created by a designer and the mask pattern actually used for exposure are so different from each other, that it is difficult to predict how the pattern will be finally formed on the wafer. Accordingly, the following steps are taken when applying the OPC to the mask pattern.
Firstly, a lithography model is made up, by incorporating both a measured value (measured CD) and a calculated value (calculated CD) of a sample mask pattern, through empirical lithography simulation. The lithography model allows, by principle, predicting a finished pattern shape of a given LSI pattern on the wafer, as long as the exposure conditions are the same as those for the sample mask pattern. Therefore, the lithography model can serve as a guideline for selection on the OPC is to be applied, and allows confirming whether the selected OPC is appropriate, through calculation of the finished pattern shape on the wafer, to be obtained by application of the selected OPC process.
Prior art related to the present invention includes Japanese Laid-open patent publication No. 2005-181636, as well as non-patented documents (Yuri Granik, Nick Cobb and Thuy Do, “Universal Process Modeling with VTRE for OPC”, Optical Micrography XV, Proceedings of SPIE Vol. 4691(2002), pp. 377-394, T. Kawazoe, K. Kobayashi, S. Takubo and M. Ohtsu, “Nonadiabatic photodissociation process using an optical near field”, J. Chem. Phy., Vol. 122, 024715 (2005), Tadashi Kawazoe et al., 2006 Spring Meeting, The Japan Society of Applied Physics, 25a-ZB-2 “Transfer of a pattern finer than 100 nm by near-field optical lithography” and Hiroki Yonemitsu et al., 2006 Spring Meeting, The Japan Society of Applied Physics, 25a-ZB-3 “Irradiation time dependence of a photosensitive region in near-field optical lithography”).
In order to properly perform the OPC, it is indispensable that the measured CD to be input to the empirical lithography simulation, and the empirical lithography simulation itself, are very accurate. The following passages cover the principle and current drawback of the simulation.
FIG. 9 illustrates, from the top, a mask pattern in a plan view, a light intensity distribution in the lithography simulation on a cross-section of a photoresist on a wafer, and a resolution pattern of the photoresist after exposure in a plan view. Although the mask pattern is usually projected on the wafer with reduction ratio of ¼ to ⅕, the projected pattern is in equal magnification in FIG. 9, for the sake of explicitness. In the case of projection lithography, if the value after the reduction is construed to represent the design value (mask CD), the description may be made hereunder as if it were the life-size case.
In FIG. 9, a wafer (not shown) is irradiated with light through an aperture of the mask, thereby presenting distribution of the light intensity depending on the location. A photochemical reaction progresses in the photoresist on the wafer depending on the light intensity such that, in a region where the quantity of reacted molecules has exceeded a certain ratio with respect to the initial total quantity of the molecules, the positive photoresist as shown in FIG. 9 is dissolved in the developing solution (in the case of a negative resist, the resist remains after the development). Accordingly, the threshold value of the quantity of the reacted molecules, which determines the resolution, corresponds to a certain light intensity value. This may be considered that a boundary in resolution is determined by a threshold value of the light intensity.
FIG. 9 is completely symmetrical. Here, the design value (mask CD) and the measured value (measured CD) are usually different. The central portion of FIG. 9 will be described in details referring to FIG. 10.
In FIG. 10, a wafer (not shown) is irradiated with light through an aperture of the mask, thereby presenting distribution of the light intensity depending on the location. A coordinate system along which the CD increases from an origin point located at the left edge of the mask will be denoted as the coordinate system x1, and a coordinate system along which the CD increases from an origin point located at the right edge of the mask will be denoted as the coordinate system x2. The coordinate of the mask can be directly read out from the design data, which is electronic data. On the other hand, although the measured value (measured CD) can be apparently obtained from the measuring equipment, the coordinate of the two edges defining that CD cannot be identified, unless measured from a reference point (fixed point) that is known to be immobile. Now, FIG. 10 shows a symmetrical pattern. Since the edges of the photoresist are considered to be located at positions respectively shifted from the two mask edges by an error value, i.e. (measured value−design value)/2 which is a negative value on the coordinate x1 and the coordinate system x2, the coordinate of the two edges can be identified. When the light intensity values (I1(x1), I2(x2)) of those photoresist edges are denoted as a threshold value Th, the photoresist edge of any mask pattern can be obtained in the lithography simulation, by applying a two-dimensional light intensity distribution to given mask pattern in the lithography simulation and identifying the edges based on the threshold value Th.
In a simplest empirical lithography simulation based on the foregoing principle, the light intensity is provided according to the optical system, and an optical parameter and an average threshold value are determined through a regression calculation or statistical process, so that the CD that is equal to the measured CD can be obtained through calculation at numerous measurement points. Such process is called a creation of a lithography model. Once the light intensity distribution and the threshold value (i.e. the lithography model) are determined, the CD in the resolution pattern of the photoresist can be predicted, with respect to a given mask.
Since the pattern shown in FIG. 10 is a symmetrical pattern, only either side may be focused on. FIG. 11 only illustrates the left side of FIG. 10. The edge of the resolution pattern of the photoresist is located at the position shifted by an error value, i.e. (measured value−design value)/2 which is a negative value on the coordinate x1, and the light intensity value I1(x1) on this edge is the threshold value Th. Thus, without the need to provide the measured CD, providing the error value leads to determination of the threshold value Th in this mask pattern.
It is clarified, however, that the threshold values vary depending on the patterns. For example, when a mask CD2 in FIG. 12 is smaller than the mask CD in FIG. 10, a threshold value in FIG. 12 is lower than the threshold value in FIG. 10. When a mask CD3 in FIG. 13 is larger than the mask CD in FIG. 10, a threshold value in FIG. 13 is higher than the threshold value in FIG. 10. The differences among FIGS. 10, 12, and 13 correspond to the differential coefficients (light intensity gradients) according to the location of I1(x1), I2(x2) on the respective threshold values. In other words, the threshold value also depends on the light intensity gradient, and is hence a value that varies depending on the location.
In this case, in the empirical lithography simulation, the light intensity is provided according to the optical system, and the threshold value Th and the light intensity gradient at the edge corresponding to that threshold value are determined at each measurement point, to thereby determine the function of the threshold value through the regression calculation or statistical process, so that the CD that is equal to the measured CD can be obtained through calculation at numerous measurement points. Once the light intensity and the threshold value—which is the function of the light intensity gradient—are determined, the CD in the resolution pattern of the photoresist can be predicted, with respect to a given mask pattern.
Actually, however, the patterns the CD of which has to be measured not only include those symmetrical patterns in which the edges are always located at positions shifted by an error value, i.e. (measured value−design value)/2 from the edge of the mask. On the contrary, the large majority of patterns are asymmetrical. FIG. 14 illustrates an asymmetric pattern. As is apparent upon comparison of FIG. 9 and FIG. 14, since the distances on the left and the right sides between adjacent apertures are different, the light intensity in the aperture illustrated in the central portion of FIG. 14 is naturally asymmetric. The central portion of FIG. 14 will be described in details referring to FIG. 15.
In FIG. 15, light passes through an aperture of the mask, thereby inducing distribution of the light intensity depending on the location. If distances L1, L2 from a fixed point to two edges are known, the respective threshold values can be obtained. In FIG. 15, the error values from the edge of the mask on the left and the right sides are different. Such state is expressed as that an edge placement error (EPE) has emerged. In the case of the asymmetric pattern, therefore, the fixed point for identifying the edge of the resolution pattern of the resist is indispensable.
An example of the fixed point is shown in FIG. 16. The fixed points are disposed at symmetrical locations in a horizontal and vertical direction, and isolated from one another on the mask so as to be free from influence of other patterns. Since the centers of the patterns remain immobile irrespective of variation in exposure intensity, these points can be utilized as an origin point of a coordinate. Here, a region is necessary for incorporating the fixed points into the mask pattern. The shorter a distance from the fixed point is, the more accurately that distance can be measured, however there are cases where the distance cannot be made shorter because of designing restriction, or where no room for incorporating the fixed point is available. Also, in the case where the fixed points are incorporated at first but removed when running the mass production, a change of the mask may cause deviation from the prediction based on the lithography model established through the lithography simulation. Thus, incorporating the fixed point imposes significant restriction on the layout design.
Although it may be possible to analyze the asymmetric pattern without incorporating the fixed point based on the fact that the measured CD and the calculated CD always agree and that the threshold value depends on the light intensity gradient, such calculation is complicated. The dependence of the threshold value on the light intensity gradient is described, for example, in Japanese Laid-open patent publication No. 2005-181636. This document discloses that the threshold value constitutes a second order function of the positional shift (error value). When the pattern is symmetrical, the positional shift can be obtained from the threshold value, because the threshold values at the two edges defining the CD are the same. When the pattern is asymmetric, however, the light intensity gradients are different and hence the threshold values are different, between the two edges defining the CD. Accordingly the positional shifts from the two edges are also different. Thus, the technique of Japanese Laid-open patent publication No. 2005-181636 is ineffective with the asymmetric pattern in obtaining the accurate threshold value and positional shift, since the disclosure is only focused on the positional shift on either edge.